Torsion units in integral group rings
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Abstract:
Let $G = \left \langle a \right \rangle \rtimes X$ where $\left \langle a \right \rangle$ is a cyclic group of order $n,X$ is an abelian group of order $m$, and $(n,m) = 1$. We prove that if $\mathbb {Z}G$ is the integral group ring of $G$ and $H$ is a finite group of units of augmentation one of $\mathbb {Z}G$, then there exists a rational unit $\gamma$ such that ${H^\gamma } \subseteq G$.References
- G. H. Cliff, S. K. Sehgal, and A. R. Weiss, Units of integral group rings of metabelian groups, J. Algebra 73 (1981), no. 1, 167–185. MR 641639, DOI 10.1016/0021-8693(81)90353-7
- I. S. Luthar and Poonam Trama, Zassenhaus conjecture for certain integral group rings, J. Indian Math. Soc. (N.S.) 55 (1990), no. 1-4, 199–212. MR 1088139
- César Polcino Milies and Sudarshan K. Sehgal, Torsion units in integral group rings of metacyclic groups, J. Number Theory 19 (1984), no. 1, 103–114. MR 751167, DOI 10.1016/0022-314X(84)90095-7
- César Polcino Milies, Jürgen Ritter, and Sudarshan K. Sehgal, On a conjecture of Zassenhaus on torsion units in integral group rings. II, Proc. Amer. Math. Soc. 97 (1986), no. 2, 201–206. MR 835865, DOI 10.1090/S0002-9939-1986-0835865-5
- Jürgen Ritter and Sudarshan K. Sehgal, On a conjecture of Zassenhaus on torsion units in integral group rings, Math. Ann. 264 (1983), no. 2, 257–270. MR 711882, DOI 10.1007/BF01457529
- Sudarshan K. Sehgal, Topics in group rings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 50, Marcel Dekker, Inc., New York, 1978. MR 508515 —, Lectures on group rings, Univ. of Palermo, 1991.
- Alfred Weiss, Rigidity of $p$-adic $p$-torsion, Ann. of Math. (2) 127 (1988), no. 2, 317–332. MR 932300, DOI 10.2307/2007056
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 1-4
- MSC: Primary 20C05; Secondary 16S34, 16U60
- DOI: https://doi.org/10.1090/S0002-9939-1994-1186996-9
- MathSciNet review: 1186996